【摘要】 推导了势流中的声波方程,并运用伽辽金加权余量法建立了相应的有限元(Finite Element Method,FEM)弱形式。对于管道声学问题的计算,给出了所需边界条件的处理方法,通过离散和装配得到有限元矩阵方程。使用自行编写的有限元程序计算分析了Herschel-Quincke(H-Q)管的消声特性。结果表明,在中低频段有限元计算结果与一维理论计算结果吻合良好,从而验证了该方法的正确性;频率较高时,两者出现明显差异,主要是由于主管和支管交接处的三维波和三维流效应所致。介质流动影响H-Q管的消声特性,特别是共振频率和通过频率,马赫数越大,影响越显著。结构形式的改变可以大大改善特定频率范围的消声性能。更多还原

【Abstract】 The sound wave equation in potential flow was derived, and its weak form of finite element method(FEM) was established by means of Galerkin weighted residual method. For the calculation of pipe acoustic problems, the treatment method of boundary conditions was given, and the finite element matrix equation was obtained with discretization and assembly. The acoustic attenuation characteristics of Herschel-Quincke(H-Q) tube was calculated and analyzed using the finite element code written by authors. The results showed that in middle and low frequency bands, the FE calculation results are in good agreement with one-dimensional theoretical calculation ones to verify the correctness of the proposed method; in higher frequency band, the obvious difference between the two is mainly due to 3-D wave and 3-D flow effects at the junction of main pipe and branch pipe; medium flow affects anechoic characteristics of H-Q tube, especially, the resonance frequency and the passing frequency are affected more significantly with increase in Mach number; the variation of structure form can greatly improve the noise elimination performance within a specific frequency range.更多还原